1 Dept. of Mechanical Engineering, University of Washington

2 Dept. of Neurosurgery, University of Washington3 Dept. of Aeronautics, Imperial College London

Towards a Multi-scale Model of Cerebral Aneurysm Evolution

Michael C Barbour1,3, Michael R. Levitt2, Spencer J. Sherwin3

Alberto Aliseda1

Whitaker Enrichment Seminar

April 27th – May 1st 2015Budapest, Hungary

Background• Cerebral aneurysms (CAs) are

found in 5-8% of the population

• 1-3% of aneurysms rupture per year

• Rupture leads to subarachnoid hemorrhaging • Mortality rates of 30-40%• Significant impairment to

survivors• Hospitalization costs - $750

million per year

Endovascular Treatment Options

• Designed to occlude flow into the aneurysm sac causing thrombosis

• Risks of associated morbidity and mortality

• Treatment is not straightforward

Coil Embolization Pipeline Embolization

Treatment Assessment Will the Aneurysm Grow to Rupture or Stabilize?

• Current prediction praxis:• Largely subjective and based on clinical experience • Size is the main determining factor (>7mm)• Inadequate - many small aneurysms rupture and large

aneurysms remain dormant

• Need more accurate and comprehensive prediction criteria

Aneurysm Pathophysiology

• Multifactorial Process• Models exist in isolation – need for coupling

H. Meng et al, AJRN, 2014

• Rupture occurs when the vascular wall can no longer withstand hemodynamic loads

Objectives

• Develop a multi-scale/multi-physics model of CA initiation and growth • Couple hemodynamics with cell dynamics• Validate model with longitudinal patient-specific data• Initiation growth

• Improve rupture prediction• Understand the processes that govern CA genesis, growth

and rupture• Simulate patient-specific progression of a CA from

genesis to rupture or stabilization

Nektar++Open source, high-order spectral/hp element framework

• Convergence and accuracy characteristics of spectral method

• Geometric flexibility of traditional finite element method

• Biomedical applications

• Efficient & highly parallelized (C++ & MPI)

• Designed for simple new model development and communication between solvers

• www.nektar.info

Vascular Wall Permeability

Aortic arch flow

Hemodynamic Model (CFD)• 3D reconstruction of vessel from rotational angiography

• Incompressible Navier-Stokes

• Time-dependent Womerlsey velocity profile at inlet

• Post-processing routines:

• Wall shear stress (WSS), oscillatory shear index (OSI), wall shear stress gradient (WSSG)

Vessel segmentation

Time-averaged WSS (Pa) and velocity streamlines

SB3C CFD Challenge• Predict rupture outcome of 5 MCA aneurysms

• High vs. Low WSS debate• Cebral JR et al. AJNR, 2011 & Xiang J et al. Stoke,

2011• Contradictory conclusions & predictions

• Hemodynamics alone are not sufficient• Need to understand the progression

Case 1 Case 2

Endothelial Cell (EC) Sensing

• WSS – mechanical stimulus for multiple vascular tone regulation pathways• Maintain vascular homeostasis

• Un-physiological WSS values lead to:• Matrix metalloproteinase activation• Smooth muscle cell apoptosis• Extracellular matrix degradation• Pro-inflammatory responses

Plata A., ICL, 2011

EC Model• WSS signaling pathways:

• Direct – activate cation channel• Indirect – release stored Ca2+

• 4 ODE’s: • 4th order Runge-Kutta• WSS and ATP dependent

Advection-Diffusion • Agonist concentration field -

Plank et al. Progress in Biophys. and Mol. Bio. 2006

EC – Hemodynamic Pipelinei. Reconstruct “healthy” vesselii. Run hemodynamic model— solve for velocity and WSSiii. Plug velocity field into advection-diffusion model — solve

for ATP concentration iv. Plug ATP and WSS into EC model

Diseased Vessel “Healthy” Vessel

Single Cell Results

Plank et al.

Elevated WSS and basal ATP

Elevated ATP and basal WSS

Solid: Dashed:

Nektar++Nektar++

Preliminary 3D Results

Time-averaged WSS (Pa)

eNOS[·]

• Direct transduction only

Conclusions/Moving Forward

• To date:• Developed new boundary conditions and post-processing

routines for hemodynamic model

• Coupled EC sensing model with hemodynamic and advection-

diffusion models

• Moving Forward:• Investigate possible correlation between eNOS concentration

and CA initiation location

• Extend cell model to include SMC apoptosis/matrix

degradation

• Solid Mechanics: Nektar++ or FEBio?

Acknowledgements

• Whitaker International Fellowship (IIE)• Sherwin Lab, Imperial College London• Dr. Spencer Sherwin• Dr. Andrew Comerford• Yumnah Mohamied• Entire Nektar++ Team

Thanks for listening!

References

• Meng H, Tutino VM, Xiang J and Siddiqui A. “High WSS or Low WSS? Complex

Interactions of Hemodynamics with Intracranial Aneurysm Initiation, Growth and

Rupture: Towards a Unifying Hypothesis.” AJNR 2014

• Plank MJ, Wall DJN and David T, “Atherosclerosis and calcium signaling in endothelial

cells.” Biophys. and Mol. Bio. 2006

• Cantwell CD, Moxey D and Sherwin SJ. “Nektar++: An open-source spectral/hp

element framework.” Computer Physics Communication 2015

• Xiang J and Menh H. “Hemodynamic-Morphologic Discriminants for Intracranial

Aneurysm Rupture.” Stroke 2011

• Cerbal JR, Mut F, Weir J, and Putman CM. “Association of Hemodynamic

Characteristics and Cerebral Aneurysm Rupture.” AJNR 2011